QUESTIONS ON PROFIT & LOSS (PART-I)

SHIV KISHOR

FORMULAS (Exemplified)

EXAMPLE QUESTIONS (SOLVED)

Question 1

If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?

A) 25% loss
B) 25% profit
C) 20% loss
D) 20% profit

Let the cost price of 1 article be Re 1
Therefore, cost price of 20 articles = 20*1 = Rs 20
The selling price of 25 articles = cost price of 20 articles = Rs 20

Now, we know the selling price of 25 articles. Let us find the cost price of 25 articles.
Cost price of 25 articles = 25*1 = Rs 25.
Therefore, profit made on sale of 25 articles = selling price of 25 articles – cost price of 25 articles
= 20 – 25 = -Rs 5

As the profit is in the negative, the merchant has made a loss of Rs 5
Therefore, % loss = loss/C)*100
% loss = -5/25*100 = 20% loss (option ‘C’)

Short trick
(20-25)*100/25 = -20 i.e. 20% loss (option ‘C’)

Question 2

Sam buys 10 apples for Re 1. At what price should he sell a dozen apples if he wishes to make a profit of 25%?

A) Re 0.125
B) Rs 1.25
C) Re 0.25
D) Rs 1.5

The cost price of 1 apple = 1/10th of a rupee or Re 0.10.
As Sam wishes to make a profit of 25%, his selling price per apple will be 0.10 + 25% of 0.10 = Re 0.125.
If the selling price of 1 apple is Re 0.125, then the selling price of a dozen apples = 12*0.125
= Rs 1.5 (option ‘D’)

Short trick
(12/10)*1.25 = Rs 1.5 (option ‘D’)

Question 3

By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What will be the percent profit made by the merchant if he sells the article at 95% of its marked price?

A) 5% profit
B) 1% loss
C) 5.5% profit
D) 4.5% profit

Let the marked price be S and the cost price of the article be C
When the merchant sells at 80% of marked price he sells at 0.8S
This results in a loss of 12%

Loss is always computed as a percentage of cost price.
Therefore, the loss incurred by the merchant = 0.12C
Hence, he will be selling the article at C – 0.12C = 0.88C when he sells at 80% of his marked price.

Equating the two sides of the relation, we get 0.8S = 0.88C
Or S = 0.88/0.8 C
Or S = 1.1C

Now, if the merchant sells at 95% of the marked price, he will be selling at 95% of 1.1C = 1.045C
Hence, the merchant will make a profit of 4.5% (option ‘D’)

Shirt trick
100[95*88/80] = 104.5 which means 4.5% profit. (option ‘D’)

Question 4

What is the maximum percentage discount that a merchant can offer on her marked price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%?

A) 50%
B) 20%
C) 16.67%
D) 33.33%

The merchant had initially marked her goods up by 50%.
Let us assume that her cost price of the goods to be 100
Therefore, a 50% mark up would have resulted in her marked price being 100 + 50% of 100 = 100 + 50 = 150.

The question states that she finally sells the product at no profit or loss. This essentially, means that she sells the product at cost price, which in this case would be 100.
Therefore, she had offered a discount of 50 on her marked price of 150.
hence discount percentage = (50/150)*100 = 33.33% (option ‘D’)

Short trick
100*[ 1 – 100/150] = 33.33% (option ‘D’)

QUERY 1

A man purchased a horse and a cow for Rs 5000. He sells the horse at 20% profit and the cow at 10% loss. If he gains 2% on the whole transaction, the cost price of the horse is?

A) Rs 2000
B) Rs 2500
C) Rs 2800
D) Rs 3000

MAHA GUPTA
Let the cost price of the horse = Rs x
Then cost price of the cow = Rs (5000 – x)

Now according to the question
20% of x – 10% of (5000 – x) = 2% of 5000

=> ^x⁄₅ – ^(5000-x)⁄₁₀ = 100

=> 2x – 5000 + x = 1000

=> x = 2000 (option ‘A’)

ALLEGATION METHOD
HORSE                                        COW

20%				-10%
		2%
2 – (-10) = 12				2 – 20 = 18

Thus, ratio of cost price of the horse and cost price of the cow = 12 : 18 = 2 : 3 

Therefore, cost price of the horse = ²⁄₅ × 5000 = Rs 2000 (option ‘A’)

TRICK
Check with answer options. Let’s take 2000 first.
Profit on 2000 = 20% of 2000 = 400
Loss on 3000 = 10% of 3000 = 300
So, overall profit = 400 – 300 =100

Profit on the whole transaction = 2% of 5000 = 100
So, it’s the correct answer option as profit on the whole transaction is the same in both ways.

QUERY 2

A man sells two horses for Rs 1710. The cost price of the first is equal to the selling price of the second. If the first is sold at 10% loss and the second at 25% gain, what is his total gain or loss (in rupees).

A) Rs 80
B) Rs 100
C) Rs 90
D) Rs 85

RONNIE BANSAL
Let the cost price (CP) of the first horse be Rs 100, then the selling price of the second (SP) of the second also will be Rs 100.

Now the selling price (SP) of the first = 100 – 10 = 90 (as the loss is 10%)
and the cost price (CP) = 100*100/125 = 80 (as the gain is 25%)

Therefore the cost price (CP) of both = 100 + 80 = 180
and the selling price (SP) 0f both = 90 = 100 = 190

Hence the profit = 190 – 180 = 10
But this profit i.e. Rs 10 is on the selling price of Rs 190
Therefore the profit on the selling price of Rs 1710 (given) will be = (10*1710)/190 = Rs 90 (option ‘C)

QUERY 3

A dealer sells a table for Rs 400, making a profit of 25%. He sells another table at a loss of 10%, and on the whole he makes neither profit nor loss. What did the second table cost him?

A) 900
B) 950
C) 1000
D) 800

Hemant Singh
SP=400 with 25% profit, it means CP=400*100/125 = 320.
So his profit = 400 – 320 = 80

Now he must loose Rs 80 in the other transaction so that there is neither profit nor loss as a whole.

So for Rs 80 loss @10% the CP = (80 x 100)/10 = 800 (option ‘D’)

QUERY 5

An article is marked for sale at Rs 275. The shopkeeper allows a discount of 5% on the marked price. His net profit is 4.5%. What did the shopkeeper pay for the article?

A) 250
B) 200
C) 225
D) 300

PRAKASH G
Marked price after discount of 5%; means the selling price of the article = 95/100*275

But his gain is 4.5%
So the cost price; means the amount paid by the shopkeeper = (95/100*275)*100/104.5 = 250 (option ‘A’)

QUERY 6

An article is sold at a certain fixed price. By selling it at 2/3 of that price, one loses 10%. The gain percent on selling it at the original price is?

A) 25%
B) 15%
C) 28%
D) 35%

Amit jha
Let the cost price be Rs 100
Thus the selling price with 10% loss = Rs 90
Means this amount of Rs 90 is 2/3 of the original selling price

So the the original selling price = 90 x 3/2 = Rs 135
Thus the gain = 135 – 100 = 35

But it’s on the cost price of Rs 100
Hence the gain in percent = 35% (option ‘D’)

QUERY 7

A man purchases a certain number of mangoes at 3 per rupee and the same number of mangoes at 4 per rupee. He mixes them together and sells them at 3 per rupee. What is his gain or loss percent?

A) 100/7
B) 50/7
C) 75/11
D) 80/11

MAHA GUPTA
Let he purchases 12 mangoes at Rs 3 per rupee and 12 mangoes at Rs 4 per rupee
Then the total cost of 12 + 12 i.e. 24 mangoes = 12/3 + 12/4 = Rs 7

But he sells them at Rs 3 per rupee
Therefore the selling price = 24/3 = 8
So it’s a profit of 8 – 7 = 1
Hence profit in percentage = (1/7) x 100 = 100/7% (option ‘A’)

QUERY 8

A merchant who marked his goods up by 50% subsequently offered a discount of 20%. What is the percentage profit that the merchant make after offering the discount?

A) 30%
B) 125%
C) 25%
D) 20% 

SHIV KISHOR
The easiest way to solve these kinds of problems is to assume a cost price for the merchant.
To make calculations easy, let us assume that the cost price = 100
The merchant marks his goods up by 50%.
Therefore, his quoted price = cost price + price marked above cost
= 100 + 50% of 100 = 100 + 50 = 150

Now, the merchant offers a discount of 20% on his quoted price
Therefore, amount of discount = 20% of 150 = 20% of 150 = 30
Therefore, he finally sells it for 150 – 30 = 120.

We assumed his cost to be 100 and he sold it finally for 120.
Therefore, his net profit = 20 on his cost of 100
Thus his profit percentage (20/100)*100 = 20% (option ‘D’)

Short Trick
[150*80/100]-100 = 20% (option ‘D’)

QUERY 9

X has bought an item of goods at 20% discount. He sold it at 40% profit on the price he bought. Find his profit in respect to original price.

A) Rs 10
B) Rs 13
C) Rs 12
D) Rs 15

Lokesh Shravan
Suppose original price = 100
But X gets it at 20% discount
So the cost price = 80

Therefore the selling price at 40% profit = 80*(140/100) = 112
So the profit in respect to original price = 112 – 100 = 12 (option ‘C’)

QUERY 10

A fruit-seller buys x guavas for Rs y and sells y guavas for Rs x. If x > y, then find his profit or loss?

A) (x² – y²)/xy % loss
B) (x² – y²)/xy % gain
C) (x² – y²)/y2 % loss
D) (x² – y²)/y2 % gain

Lokesh Shravan
Let the seller buys xy guavas (take LCM of x & y to make the calculation easier)

Now we have to find the profit earned or loss suffered, so we need to know the cost price as well as the selling price.

Thus the CP of xy guavas = y/x*xy = y²
and the SP of xy guavas = x/y*xy = x²

As x is greater than y, so the selling price is more than the cost price. Obviously it will be a gain.
So gain = x² – y²
and gain in percentage = [(x² – y²)/y²]*100 = (x² – y²)/y² % (option ‘D’)